Proceedings of SALT 30: 624–644, 2020 Simplification is not scalar strengthening* Paolo Santorio University of Maryland, College Park Abstract We show that Simplification of Disjunctive antecedents is not a scalar inference. The argument exploits information-sensitive modals, like epistemic probably and deliberative ought. When items of this sort are the main modal of a conditional, we can have that: (a) pif A or B, MODAL Cq is true; (b) the basic meaning computed via classical semantics for conditionals and disjunction is false. This combination is impossible on any scalar account of Simplification: scalar inferences are strengthenings, hence the output of scalar inferences must entail the basic meaning of a sentence. We suggest an account of Simplification based on alternative semantics, and show how this account can be made compatible with old and new counterexamples to Simplification. Keywords: conditionals, simplification of disjunctive antecedents, scalar implicature, free choice, information sensitivity. 1 Introduction Simplification of Disjunctive Antecedent (‘Simplification’ for short) is the inference from a conditional with a disjunctive antecedent to the ‘simplified’ conditionals whose antecedents are the individual disjuncts. A typical example of Simplification is in (1), which involves would-conditionals. (1) If it rained or snowed, the game would be cancelled. a. If it rained, the game would be cancelled. b. If it snowed, the game would be cancelled. Simplification appears to be a sound inference. But accounts that treats Simplifi- cation as semantically valid run into problems. The validity of Simplification is incompatible with two other widely held principles about conditionals. In particular, as I explain in §2, Simplification cannot be a valid inference on a standard possible worlds semantics for conditionals based on comparative closeness, in the style of Stalnaker, Kratzer, and Lewis. * Thanks to Fabrizio Cariani, Lucas Champollion, Moysh Bar-Lev, and Jacopo Romoli and the audience of SALT 30 for useful comments. ©2020 Santorio Simplification is not scalar strengthening In the face of this difficulty, the literature has gone in two opposite directions. Some theorists abandon standard intensional semantics in favor of frameworks that exploit more fine-grained notions of meaning (usually, truthmaker or inquisitive semantics). Other theorists preserve standard possible worlds semantics for condi- tionals, but try to recapture Simplification as a kind of scalar inference. In outline, the idea is to treat Simplification as an optional effect that is triggered by the same mechanisms that generate standard scalar implicatures, like the inference from (2a) to (2b). (2) a. Maria ate some of the cookies b. Maria ate some but not all of the cookies. The goal of this paper is to put forward a conclusive argument against the scalar account. The argument exploits information-sensitive modals, like epistemic probably and deliberative ought. When items of this sort are the main modal of a conditional, we can have the following combination: (a) a conditional pif A or B, MODAL Cq has a true reading; (b) the basic meaning of the same conditional is false. This combination is simply impossible on any scalar account of Simplification. On any theory of scalar inferences, whether semantic or pragmatic, scalar inferences strengthen the basic meaning of a sentence. But information-sensitive modals show precisely that the Simplification-producing reading is not always a strengthening of the standard possible worlds meaning of a conditional. The upshot is that Simplification is not a scalar inference, and the only route available for a theory of Simplification is the semantic one. I proceed as follows. In §2, I set up some background about Simplification and scalar implicature. In §3, I give the argument against scalar theories of Simplification. In §4, I consider how the scalar theorist might resist the argument. In §5, I show how semantic accounts of Simplification can account for one of the data points that appear to favor a scalar account, i.e. the fact that Simplification disappears in a restricted range of cases. 2 Background: Simplification and Scalar Implicature 2.1 Simplification and possible worlds semantics for conditionals Simplification of Disjunctive Antecedents is the following inference pattern: Simplification of Disjunctive Antecedents If A or B, MOD C If A, MOD C, If B, MOD C (For discussion of Simplification see, among many, Fine 1975; McKay & Van In- wagen 1977; Alonso-Ovalle 2009; Ciardelli, Zhang & Champollion 2018.) Sim- 625 Santorio plification is validated by virtually all types of conditionals in natural language, independently of the choice of the main modal. For a few examples: sentences (3)–(5) show that Simplification occurs in bare indicatives like (3), counterfactuals like (4), and conditionals whose main modal is a probability adverb like (5). (3) If it rained or snowed, the game was cancelled. a. If it rained, the game was cancelled. b. If it snowed, the game was cancelled. (4) If it had rained or snowed, the temperature would have fallen. a. If it had rained, the temperature would have fallen. b. If it had snowed, the temperature would have fallen. (5) If it rained or snowed, probably it was windy too. a. If it rained, probably it was windy too. b. If it snowed, probably it was windy too. Unfortunately, Simplification is hard to capture in classical frameworks for the semantics of conditionals (such as the ones developed by Stalnaker 1968, Lewis 1973, Kratzer 1986, 2012). The reason is that the validity of Simplification is incompatible with two other logical principles that are commonly assumed to hold for at least some central types of conditionals. These principles are: + + Failure of Antecedent Strenghtening If A, MOD C 6 If A , MOD C (with A A) 0 0 Substitution If A, MOD C If A , MOD C (with A A ) Let me quickly review the arguments in support these principles. Substitution says that clauses that are logically equivalent are substitutable in the antecedents of conditionals. This property is vindicated by any semantics that is intensional, i.e. any semantics that treats clauses that are true and false in the same set of worlds as equivalent. Failure of Antecedent Strengthening says that the inference from a conditional + pIf A, MOD Cq to a conditional with a stronger antecedent pIf A , MOD Cq is invalid. The observation that Antecedent Strengthening fails is at the basis of modern literature about conditionals (and in particular, counterfactuals). The data produced in its support typically involve Sobel sequences, i.e. sequences of conditionals like (6): (6) a. If it rained, the game would still happen. b. If it rained and the stadium exploded, the game would be called off. 626 Simplification is not scalar strengthening The two conditionals in (6) appear to be consistent. Yet, if Antecedent Strengthening was valid, (6a) should entail If it rained and the stadium exploded, the game would still happen, which is incompatible with (6b).1 Hence Antecedent Strengthening appears to be invalid for would-conditionals like those in (6).2 Possible worlds semantics for conditionals aim just at capturing the failure of antecedent strengthening in an intensional setting. It’s useful to give a concrete example of a semantics for conditionals in this mold. The basic idea is that a conditional pIf A, MOD Cq quantifies over the closest A-verifying worlds to the actual world, and asserts that all those worlds are C-verifying worlds. Formally, the semantics appeals to a relation of comparative closeness between worlds, symbolized as ‘w’. w compares worlds with respect to their closeness 0 00 0 00 to a benchmark world w: w w w says that w is closer to w than w . The basic function of w is singling out a set of worlds that verify the antecedent and that at the same time are ‘maximal’, i.e. are such that no other world is more similar to w then they are. Conditionals quantify over the maximal set of worlds so individuated. Using, as is standard, ‘ ’ and ‘ ’ for the interpretation function, here are schematic truth conditions:3 J K (7) If A, MOD C ;w= true iff J 0 K 0 ;w0 ;w0 for all w 2 maxw ({w : A = true}), C = true 0 J;w0K J K (where maxw ({w : A = true}) is the set of closest A-worlds) J K Semantics like those in (7) can be taken as a template for the semantics of a variety of conditional sentences. Following the basic line of thought in Kratzer 1986, we can predict the difference between conditionals of different flavors by assuming that context supplies different relations of comparative closeness. Now, the semantics in (7) validates Failure of Antecedent Strengthening and Substitution. The former is validated because different antecedents may quantify over different sets of closest worlds. In particular, if the closest A-worlds do not include A ^ B-worlds, we can have that pIf A, MOD Cq is true while pIf A ^ B, MOD Cq is false. The latter is validated because the semantics is intensional, and 1 At least, assuming the principle of Conditional Non-Contradiction: if A is possible, If A, MOD C ^ If A, MOD :C ?. 2 A number of recent theories of counterfactuals adopt a strict conditional semantics, which does vindicate Antecedent Strengthening, and relocate the explanation for the nonmonotonicity observed in (6) in discourse dynamics. See von Fintel 2001; Gillies 2007 for discussion. For current purposes, these accounts are still problematic. Since they do recognize a level of meaning at which Antecedent Strengthening fails, they do not explain why the inference from a counterfactual with a disjunctive antecedent to a ‘simplified’ counterfactual appears valid. 3 This is an approximation to both of Stalnaker and Lewis’s accounts. For Stalnaker, the ordering singles out, for each world w, a unique world w0 that is closest to it.